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Assume that the number of messages input to a communication channel in an interval of duration t seconds is Poisson distributed with parameter 0

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Assume that the number of messages input to a communication channel in an interval of duration t seconds is Poisson distributed with parameter 0.4t. Compute the probabilities of the following events:

(a) exactly three messages will arrive during a 10-second interval;

(b) more than three messages will arrive during a 10-second interval;

(c) 10 seconds will pass without a message;

(d) a message will arrive in the next 10 seconds, if 5 seconds have already gone by without a message.